The Holmes–Thompson Area of $$\ell^1_4$$ Is Not Totally Convex

We prove that the Holmes–Thompson area of the hypermetric space $$\ell^1_4$$ is not totally convex. This means that for some planes in this space, there are no linear projections onto them that minimize the Holmes–Thompson area.

Authors

Institutions

Publication Details

Journal
Proceedings of the Steklov Institute of Mathematics
Published
2025-12-01
DOI
https://doi.org/10.1134/s0081543825601418
Primary Topic
Advanced Banach Space Theory
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

The Holmes–Thompson Area of $$\ell^1_4$$ Is Not Totally Convex

I. M. Vasilyev
Proceedings of the Steklov Institute of Mathematics
Advanced Banach Space Theory
article

The Holmes–Thompson Area of $$\ell^1_4$$ Is Not Totally Convex

I. M. Vasilyev
article en

Abstract

We prove that the Holmes–Thompson area of the hypermetric space $$\ell^1_4$$ is not totally convex. This means that for some planes in this space, there are no linear projections onto them that minimize the Holmes–Thompson area.

Proceedings of the Steklov Institute of MathematicsVol. 331(1)
Russian Academy of Sciences (RU), Steklov Mathematical Institute (RU)
Openalex Percentile: Top 16%
Advanced Banach Space Theory
DOISourceOpenAlex
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.